Sorry if this is too simple question, but I am new to AI. I am just learning ML of Professor Andrew Ng. In the following code of gradient descent, why do we write i<100000? Where did this 100000 number come from? Also, what is the logic behind if “i% math.ceil(num_iters/10) == 0” condition?
There are more doubt below this code.
def gradient_descent(x, y, w_in, b_in, alpha, num_iters, cost_function, gradient_function):
"""
Performs gradient descent to fit w,b. Updates w,b by taking
num_iters gradient steps with learning rate alpha
Args:
x (ndarray (m,)) : Data, m examples
y (ndarray (m,)) : target values
w_in,b_in (scalar): initial values of model parameters
alpha (float): Learning rate
num_iters (int): number of iterations to run gradient descent
cost_function: function to call to produce cost
gradient_function: function to call to produce gradient
Returns:
w (scalar): Updated value of parameter after running gradient descent
b (scalar): Updated value of parameter after running gradient descent
J_history (List): History of cost values
p_history (list): History of parameters [w,b]
"""
# An array to store cost J and w's at each iteration primarily for graphing later
J_history = []
p_history = []
b = b_in
w = w_in
for i in range(num_iters):
# Calculate the gradient and update the parameters using gradient_function
dj_dw, dj_db = gradient_function(x, y, w , b)
# Update Parameters using equation (3) above
b = b - alpha * dj_db
w = w - alpha * dj_dw
# Save cost J at each iteration
if i<100000: # prevent resource exhaustion
J_history.append( cost_function(x, y, w , b))
p_history.append([w,b])
# Print cost every at intervals 10 times or as many iterations if < 10
if i% math.ceil(num_iters/10) == 0:
print(f"Iteration {i:4}: Cost {J_history[-1]:0.2e} ",
f"dj_dw: {dj_dw: 0.3e}, dj_db: {dj_db: 0.3e} ",
f"w: {w: 0.3e}, b:{b: 0.5e}")
return w, b, J_history, p_history #return w and J,w history for graphing
Also, why do we put iterations=10000 in the following code? How do we know what value to put?
# initialize parameters
w_init = 0
b_init = 0
# some gradient descent settings
iterations = 10000
tmp_alpha = 1.0e-2
# run gradient descent
w_final, b_final, J_hist, p_hist = gradient_descent(x_train ,y_train, w_init, b_init, tmp_alpha,
iterations, compute_cost, compute_gradient)
print(f"(w,b) found by gradient descent: ({w_final:8.4f},{b_final:8.4f})")
How do we get the values of y-axis, which is cost, of the both the graphs? I couldn’t figure it out from the code. The code and output both are given:
# plot cost versus iteration
fig, (ax1, ax2) = plt.subplots(1, 2, constrained_layout=True, figsize=(12,4))
ax1.plot(J_hist[:100])
ax2.plot(1000 + np.arange(len(J_hist[1000:])), J_hist[1000:])
ax1.set_title("Cost vs. iteration(start)"); ax2.set_title("Cost vs. iteration (end)")
ax1.set_ylabel('Cost') ; ax2.set_ylabel('Cost')
ax1.set_xlabel('iteration step') ; ax2.set_xlabel('iteration step')
plt.show()
